An EM Algorithm for Estimating Equations

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Journal Article
Journal of Computational and Graphical Statistics, 2004, 13 (1), pp. 48 - 65
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This article presents an algorithm for accommodating missing data in situations where a natural set of estimating equations exists for the complete data setting. The complete data estimating equations can correspond to the score functions from a standard, partial, or quasi-likelihood, or they can be generalized estimating equations (GEEs). In analogy to the EM, which is a special case, the method is called the ES algorithm, because it iterates between an E-Step wherein functions of the complete data are replaced by their expected values, and an S-Step where these expected values are substituted into the complete-data estimating equation, which is then solved. Convergence properties of the algorithm are established by appealing to general theory for iterative solutions to nonlinear equations. In particular, the ES algorithm (and indeed the EM) are shown to correspond to examples of nonlinear Gauss-Seidel algorithms. An added advantage of the approach is that it yields a computationally simple method for estimating the variance of the resulting parameter estimates.
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